Suppose that each source s_i in a flow network with multiple sources and sinks produces exactly p_i units of flow, so that ∑_ν∈v f(s_i, v)= P_i. Suppose also that each sink t_j consumes exactly q_j units, so that that ∑_ν∈v f(ν, t_j) = q_j, where ∑_i P_i = ∑_{j qj}. Show how to convert the problem of finding a flow f that obeys these additional constraints into the problem of finding a maximum flow in a singlesource, single-sink flow network.